Pai Gow Tiles Banking Questions

If anyone has the time to work this out I'd really appreciate it!

Assuming that I'm banking, what is the EV relative to the number of players I bank against including the dealer? For simplicity's sake, assume we're all playing optimally. 6 spot table, 5% commission on net win.

Quote: chrisjs87

If anyone has the time to work this out I'd really appreciate it!

Assuming that I'm banking, what is the EV relative to the number of players I bank against including the dealer? For simplicity's sake, assume we're all playing optimally. 6 spot table, 5% commission on net win.

I do not know the exact answer to your question, but I can guide you as follows:

1. The more HANDS you are banking against, the better. You have a higher expectation playing against 5 hands of $20 than 1 hand of $100.

2. Assuming YOU are playing optimally, and the dealer is playing the house way, the house edge is 1.66% when not banking, and -0.20% when banking.

That means if somehow you could dictate the dealer bet against you however much you want, you can be sure to break even if he bets 8.3 times your last bet.

So the takeaway here is that if you can book at least 8.3 times your bet when banking, you definitely have the edge -- and the more people you play against, the better. The ratio is likely much lower to have the edge the more people you play against.

Also, your true expectation will be higher than expected because of dealer errors and players setting their hands horribly.

I would also be interested in knowing the exact answer for the number of players like the Wizard's chart for PGP:



Wizard? JB? Anyone?

You are correct that there is an advantage of taking the bank due to Bank Wins Ties and House-Way inefficiencies. I think the question is, assuming everyone is playing perfect (or identical) strategy - what is the house edge. One factor is that when banking you are only taxed on the net profit, so if you lost to half and won the others you would not pay any commission.

Assuming, to make things simpler it was a totally fair game, you won 30%, lost 30% and tied 40% (based on wizard's numbers https://wizardofodds.com/games/pai-gow-tiles/ ) then look at two options.
(a) Playing against one player betting £600. The expected loss is £9 (=P(Win)*Tax*Bet = 30% * 5% * £600).
(b) Playing against six players each betting £100. The expected loss is £3.73.

Saying that the other players will be using optimal strategy is vague; optimal against what? The house way? Your strategy? What is your strategy optimal against?

All of the strategies you are playing against need to be absolute (like the house way), otherwise a circular situation appears:

#1: Dealer uses house way
#2: You use optimal player-banker strategy against the house way
#3: Other players use optimal strategy against your strategy ---> now your strategy is not optimal against the players
#4: You adjust your strategy to account for the strategy the players are using ---> now their strategy is not optimal against yours
#5: repeat #3 and #4 ad infinitum

It would be best to specify precisely what strategy the other players will be using, as well as how much you and they are betting per hand. Then the question would best be answered via simulation, because there are too many combinations to do an exhaustive analysis in a timely manner.

In my experience, most other players do not stray very far from house way.

I think the most useful simulation would be:

1. You bet table minimum when dealer is banking. You play optimal against the dealer's house way.
2. You bank every other hand. You play optimal against house way. Dealer and other players play house way.
3. The dealer and N other players all bet the table minimum against you.


You could also manipulate #3 to have the players betting more than the table minimum against you as that happens frequently.

Quote: sodawater

In my experience, most other players do not stray very far from house way.

From what I have observed, I mostly agree. The average player usually only deviates from the house way to play 6/7 or better instead of a H8 Gong.

Quote: JB

From what I have observed, I mostly agree. The average player usually only deviates from the house way to play 6/7 or better instead of a H8 Gong.

I agree, the average player does make that deviation. Maybe bake that into the sim. if you do one...

Quote: JB

Saying that the other players will be using optimal strategy is vague; optimal against what? The house way? Your strategy? What is your strategy optimal against?

All of the strategies you are playing against need to be absolute (like the house way), otherwise a circular situation appears:

#1: Dealer uses house way
#2: You use optimal player-banker strategy against the house way
#3: Other players use optimal strategy against your strategy ---> now your strategy is not optimal against the players
#4: You adjust your strategy to account for the strategy the players are using ---> now their strategy is not optimal against yours
#5: repeat #3 and #4 ad infinitum

It would be best to specify precisely what strategy the other players will be using, as well as how much you and they are betting per hand. Then the question would best be answered via simulation, because there are too many combinations to do an exhaustive analysis in a timely manner.

JB, thanks for taking the time to respond. Earlier in this thread there was a post made showing the banker advantage based on the numbers of players for Pai Gow Poker... I'm basically looking for a chart like that, only for tiles. It would be interesting (at least for me) to be able to adjust different strategies for the players/banker, bet sizes and etc to see a much larger picture, but I would imagine that would be an exhausting project to undertake. So if there's anyway to generically state what the player-banker's advantage is relative to the number of players, that would still be helpful.

Quote: chrisjs87

JB, thanks for taking the time to respond. Earlier in this thread there was a post made showing the banker advantage based on the numbers of players for Pai Gow Poker... I'm basically looking for a chart like that, only for tiles. It would be interesting (at least for me) to be able to adjust different strategies for the players/banker, bet sizes and etc to see a much larger picture, but I would imagine that would be an exhausting project to undertake. So if there's anyway to generically state what the player-banker's advantage is relative to the number of players, that would still be helpful.

Agree, I would also love exactly such a chart.

I'm afraid that I haven't worked out the house edge for banking against more than one player at a time. For one thing, I sense that it causes tension when as a white player I ask to bank when there are already Asian players at the table. They almost always hate it when I do that. So, I think you'll find it difficult to bank against a bunch of strangers. The Los Angeles casinos may be different, where the players are required to bank.

If you bank enough times in a row they will start to bet against you.

remember, whites bank because its the right play....Asians bank on superstition

Quote: Wizard

I'm afraid that I haven't worked out the house edge for banking against more than one player at a time. For one thing, I sense that it causes tension when as a white player I ask to bank when there are already Asian players at the table. They almost always hate it when I do that. So, I think you'll find it difficult to bank against a bunch of strangers. The Los Angeles casinos may be different, where the players are required to bank.

As both a dealer and floor and I've noticed that the tension arises regardless of race. If one player doesn't want another to bank, they'll intentionally place a bet that their opponent can't/won't cover or complain in their respective language.

I'd still really like to see the effect this has on house edge, but if no one has the time I completely understand.

Quote: sodawater

That means if somehow you could dictate the dealer bet against you however much you want, you can be sure to break even if he bets 8.3 times your last bet.

There is no somehow. Casinos don't allow you to bank more than you bet in the last hand when the dealer was banking.